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Nom de l'assignatura: Tècniques Matemàtiques i Estadístiques

Codi de l'assignatura: 568423

Curs acadèmic: 2019-2020

Coordinació: Francesc Xavier Luri Carrascoso

Departament: Departament de Física Quàntica i Astrofísica

crèdits: 6

Programa únic: S

 

 

Hores estimades de dedicació

Hores totals 150

 

Activitats presencials

60

 

-  Teoria

 

60

Treball tutelat/dirigit

40

Aprenentatge autònom

50

 

 

Recomanacions

 


We recommend to have basic programming skills to follow this course.

 

 

Competències que es desenvolupen

 


* Understand a problem, connect it with acquired knowledge, propose a solution and test it.

* Follow a course given in English.

* Follow (slightly) abstract arguments leading to fundamental theorems, understand their meaning, and how to use them e.g. in a physical context.

* Basic programming skills and usage of basic tools for handling of data (generation of graphics and handling of data files).

* Basic calculus.

 

 

 

 

Objectius d'aprenentatge

 

Referits a coneixements


* To get acquainted with fundamental results of Probability Theory and Statistics. To understand their relevance to important issues in experimental and     theoretical physics.

* To understand the power and limitations of Monte-Carlo methods, in particular when applied to physical contexts, such as quantum field theory.

* To develop comprehensive skills on the topic, ranging from the ability to use software (such as R) to perform computations on specific data to the ability to prove easy mathematical statements in order to solve theoretical issues.

* To get acquainted with the techniques for data analysis and the basic concepts of data mining.

 

 

Blocs temàtics

 

1. Fundamental of Probability Theory and Statistics

*  * General review of probability theory: Random variables and events. Bayes theorem. Probability distributions: binomial, Poisson, Gaussian, Cauchy. Law of large numbers. Hoeffding’s inequality. Central-limit theorem and Berry-Eseen theorem.

* Introduction to R.

* Statistical inference: Point Estimation Theory, Confidence Intervals, Chi-2 tests, Fisher Information, Cramer-Rao bound, Maximum-likelihood estimators, hypothesis testing, Kolmogorov-Smirnov Tests, Least Squares, Information Theory (Typicality, mutual information, correlations).

2. Monte Carlo Methods

*  * Generalities. Sampling, Integration, Optimisation.

* Importance sampling, stratified sampling, rejection sampling.

* Metropolis algorithm. Generalities: reversibility, strong ergodicity and convergence. A priori probabilities, parallel tempering, simulated annealing.

* Applications of the Metropolis algorithm to statistical Physics, quantum field theory and events generation.

3. Multivariate analysis and statistical treatment techniques

*  * Data analysis and representation. Statistical distances. Principal component analysis.
* Hierarchical and non-hierarchical clustering.
* Discriminant analysis.
* Neural networks.
* Support vector machines.
* Non-parametric methods of estimation of a probability density function: histograms, simple estimators, kernel estimators.

4. Databases and data mining

*  * Basic concepts
* Introduction to data mining
* Case study: the Gaia archive.

5. Practical Work

*  * Introduction to R
* Introduction to WEKA (data analysis and data mining)

 

 

Avaluació acreditativa dels aprenentatges

 

There will be no exam for this course. Instead, 5 problem assignments will be given during the course. Grading will be based on the evaluation of the reports provided.

Re-evaluation: the student will have to redo and resubmit the 5 problem assignments correcting them according to the instructions from the teachers. Once they are received they will be evaluated and the student will pass an oral exam on their contents. If this exam is successfully passed the mark of the course will be fixed from the marks of the assignments, otherwise the subject will be graded as non-passed.

 

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